Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem

Anastasiia Vasylchenkova; Jaroslaw E. Prilepsky; Sergei K. Turitsyn

doi:10.1364/OL.43.003690

Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem

Anastasiia Vasylchenkova^*, Jaroslaw E. Prilepsky, Sergei K. Turitsyn

^*Corresponding author for this work

Aston Institute of Photonic Technologies (AiPT)

Research output: Contribution to journal › Article › peer-review

Abstract

We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov–Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather’s multiple eigenvalue. We also study the impact of additive white Gaussian noise on the stability of numerical eigenvalues computation.

Original language	English
Pages (from-to)	3690-3693
Number of pages	4
Journal	Optics Letters
Volume	43
Issue number	15
Early online date	3 Jul 2018
DOIs	https://doi.org/10.1364/OL.43.003690
Publication status	Published - 27 Jul 2018

Bibliographical note

©2018 Optical Society of America]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.

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10.1364/OL.43.003690

Contour integrals for numerical computation
©2018 Optical Society of America]. One print or electronic copy may be made for personal use only. Systematic reproduction and distribution, duplication of any material in this paper for a fee or for commercial purposes, or modifications of the content of this paper are prohibited.
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Cite this

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abstract = "We propose a novel algorithm for the numerical computation of discrete eigenvalues in the Zakharov–Shabat problem. Our approach is based on contour integrals of the nonlinear Fourier spectrum function in the complex plane of the spectral parameter. The reliability and performance of the new approach are examined in application to a single eigenvalue, multiple eigenvalues, and the degenerate breather{\textquoteright}s multiple eigenvalue. We also study the impact of additive white Gaussian noise on the stability of numerical eigenvalues computation.",

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Contour integrals for numerical computation of discrete eigenvalues in the Zakharov–Shabat problem

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